login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A266787
Binary representation of the n-th iteration of the "Rule 61" elementary cellular automaton starting with a single ON (black) cell.
2
1, 11, 1100, 1010111, 1111000, 11010001111, 1111010000, 111010001111111, 1111010000000, 1111010001111111111, 1111010000000000, 11111010001111111111111, 1111010000000000000, 111111010001111111111111111, 1111010000000000000000, 1111111010001111111111111111111
OFFSET
0,2
FORMULA
Conjectures from Colin Barker, Jan 03 2016 and Apr 18 2019: (Start)
a(n) = 11001*a(n-2)-10011000*a(n-4)+10000000*a(n-6) for n>10.
G.f.: (1 +11*x -9901*x^2 +889100*x^3 -979100*x^4 +7891000*x^5 -109001000*x^6 +1090110000*x^7 +9990000*x^8 -1100000000*x^9 +100000000*x^10) / ((1 -x)*(1 +x)*(1 -100*x)*(1 +100*x)*(1 -1000*x^2)).
(End)
MATHEMATICA
rule=61; rows=20; ca=CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]], {rows-k+1, rows+k-1}], {k, 1, rows}]; (* Truncated list of each row *) Table[FromDigits[catri[[k]]], {k, 1, rows}] (* Binary Representation of Rows *)
CROSSREFS
Sequence in context: A319424 A348269 A153435 * A109227 A133342 A110574
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 03 2016
STATUS
approved